Our technical contribution is also related to the literature on differentiable ranking, which includes a large body of work on approximating learning-to-rank metrics [1]}, [2]}, [3]}, and recent growing interest in designing smooth ranking modules [4]}, [5]}, [6]} for end-to-end differentiation pipelines. The closest method to ours is the differentiable sorting operator of [6]}, which also relies on isotonic regression. The differences between our approaches are explained in Remark REF .
